LMFDB - Embedded newform 4006.2.a.g.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0106586 q^{3} +1.00000 q^{4} -1.19509 q^{5} +0.0106586 q^{6} +1.61812 q^{7} -1.00000 q^{8} -2.99989 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0106586 q^{3} +1.00000 q^{4} -1.19509 q^{5} +0.0106586 q^{6} +1.61812 q^{7} -1.00000 q^{8} -2.99989 q^{9} +1.19509 q^{10} -2.53909 q^{11} -0.0106586 q^{12} +6.61830 q^{13} -1.61812 q^{14} +0.0127380 q^{15} +1.00000 q^{16} -1.49307 q^{17} +2.99989 q^{18} +1.43647 q^{19} -1.19509 q^{20} -0.0172469 q^{21} +2.53909 q^{22} -0.350766 q^{23} +0.0106586 q^{24} -3.57176 q^{25} -6.61830 q^{26} +0.0639505 q^{27} +1.61812 q^{28} +1.92959 q^{29} -0.0127380 q^{30} -6.77963 q^{31} -1.00000 q^{32} +0.0270632 q^{33} +1.49307 q^{34} -1.93380 q^{35} -2.99989 q^{36} -0.851075 q^{37} -1.43647 q^{38} -0.0705420 q^{39} +1.19509 q^{40} +2.50850 q^{41} +0.0172469 q^{42} +7.23779 q^{43} -2.53909 q^{44} +3.58514 q^{45} +0.350766 q^{46} -2.38199 q^{47} -0.0106586 q^{48} -4.38170 q^{49} +3.57176 q^{50} +0.0159141 q^{51} +6.61830 q^{52} -5.21338 q^{53} -0.0639505 q^{54} +3.03444 q^{55} -1.61812 q^{56} -0.0153108 q^{57} -1.92959 q^{58} +8.44227 q^{59} +0.0127380 q^{60} +12.5641 q^{61} +6.77963 q^{62} -4.85417 q^{63} +1.00000 q^{64} -7.90948 q^{65} -0.0270632 q^{66} -7.90704 q^{67} -1.49307 q^{68} +0.00373868 q^{69} +1.93380 q^{70} -7.53708 q^{71} +2.99989 q^{72} -9.66738 q^{73} +0.851075 q^{74} +0.0380700 q^{75} +1.43647 q^{76} -4.10855 q^{77} +0.0705420 q^{78} +15.2302 q^{79} -1.19509 q^{80} +8.99898 q^{81} -2.50850 q^{82} -1.88445 q^{83} -0.0172469 q^{84} +1.78436 q^{85} -7.23779 q^{86} -0.0205667 q^{87} +2.53909 q^{88} -10.1245 q^{89} -3.58514 q^{90} +10.7092 q^{91} -0.350766 q^{92} +0.0722615 q^{93} +2.38199 q^{94} -1.71671 q^{95} +0.0106586 q^{96} +7.33946 q^{97} +4.38170 q^{98} +7.61698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.0106586	−0.00615375	−0.00307688	−	0.999995i	$-0.500979\pi$
$3$	−0.0106586	−0.00615375	−0.00307688	+	0.999995i	$0.500979\pi$
$4$	1.00000	0.500000
$5$	−1.19509	−0.534461	−0.267230	−	0.963633i	$-0.586108\pi$
$5$	−1.19509	−0.534461	−0.267230	+	0.963633i	$0.586108\pi$
$6$	0.0106586	0.00435136
$7$	1.61812	0.611591	0.305795	−	0.952097i	$-0.401078\pi$
$7$	1.61812	0.611591	0.305795	+	0.952097i	$0.401078\pi$
$8$	−1.00000	−0.353553
$9$	−2.99989	−0.999962
$10$	1.19509	0.377921
$11$	−2.53909	−0.765565	−0.382782	−	0.923839i	$-0.625034\pi$
$11$	−2.53909	−0.765565	−0.382782	+	0.923839i	$0.625034\pi$
$12$	−0.0106586	−0.00307688
$13$	6.61830	1.83559	0.917794	−	0.397058i	$-0.129969\pi$
$13$	6.61830	1.83559	0.917794	+	0.397058i	$0.129969\pi$
$14$	−1.61812	−0.432460
$15$	0.0127380	0.00328894
$16$	1.00000	0.250000
$17$	−1.49307	−0.362123	−0.181062	−	0.983472i	$-0.557953\pi$
$17$	−1.49307	−0.362123	−0.181062	+	0.983472i	$0.557953\pi$
$18$	2.99989	0.707080
$19$	1.43647	0.329549	0.164774	−	0.986331i	$-0.447310\pi$
$19$	1.43647	0.329549	0.164774	+	0.986331i	$0.447310\pi$
$20$	−1.19509	−0.267230
$21$	−0.0172469	−0.00376358
$22$	2.53909	0.541336
$23$	−0.350766	−0.0731397	−0.0365699	−	0.999331i	$-0.511643\pi$
$23$	−0.350766	−0.0731397	−0.0365699	+	0.999331i	$0.511643\pi$
$24$	0.0106586	0.00217568
$25$	−3.57176	−0.714352
$26$	−6.61830	−1.29796
$27$	0.0639505	0.0123073
$28$	1.61812	0.305795
$29$	1.92959	0.358315	0.179158	−	0.983820i	$-0.442663\pi$
$29$	1.92959	0.358315	0.179158	+	0.983820i	$0.442663\pi$
$30$	−0.0127380	−0.00232563
$31$	−6.77963	−1.21766	−0.608829	−	0.793302i	$-0.708360\pi$
$31$	−6.77963	−1.21766	−0.608829	+	0.793302i	$0.708360\pi$
$32$	−1.00000	−0.176777
$33$	0.0270632	0.00471110
$34$	1.49307	0.256060
$35$	−1.93380	−0.326871
$36$	−2.99989	−0.499981
$37$	−0.851075	−0.139916	−0.0699579	−	0.997550i	$-0.522287\pi$
$37$	−0.851075	−0.139916	−0.0699579	+	0.997550i	$0.522287\pi$
$38$	−1.43647	−0.233026
$39$	−0.0705420	−0.0112958
$40$	1.19509	0.188960
$41$	2.50850	0.391762	0.195881	−	0.980628i	$-0.437243\pi$
$41$	2.50850	0.391762	0.195881	+	0.980628i	$0.437243\pi$
$42$	0.0172469	0.00266125
$43$	7.23779	1.10375	0.551877	−	0.833926i	$-0.313912\pi$
$43$	7.23779	1.10375	0.551877	+	0.833926i	$0.313912\pi$
$44$	−2.53909	−0.382782
$45$	3.58514	0.534441
$46$	0.350766	0.0517176
$47$	−2.38199	−0.347449	−0.173724	−	0.984794i	$-0.555580\pi$
$47$	−2.38199	−0.347449	−0.173724	+	0.984794i	$0.555580\pi$
$48$	−0.0106586	−0.00153844
$49$	−4.38170	−0.625957
$50$	3.57176	0.505123
$51$	0.0159141	0.00222842
$52$	6.61830	0.917794
$53$	−5.21338	−0.716112	−0.358056	−	0.933700i	$-0.616560\pi$
$53$	−5.21338	−0.716112	−0.358056	+	0.933700i	$0.616560\pi$
$54$	−0.0639505	−0.00870256
$55$	3.03444	0.409164
$56$	−1.61812	−0.216230
$57$	−0.0153108	−0.00202796
$58$	−1.92959	−0.253367
$59$	8.44227	1.09909	0.549545	−	0.835464i	$-0.314801\pi$
$59$	8.44227	1.09909	0.549545	+	0.835464i	$0.314801\pi$
$60$	0.0127380	0.00164447
$61$	12.5641	1.60866	0.804332	−	0.594180i	$-0.202523\pi$
$61$	12.5641	1.60866	0.804332	+	0.594180i	$0.202523\pi$
$62$	6.77963	0.861014
$63$	−4.85417	−0.611568
$64$	1.00000	0.125000
$65$	−7.90948	−0.981050
$66$	−0.0270632	−0.00333125
$67$	−7.90704	−0.965999	−0.483000	−	0.875621i	$-0.660453\pi$
$67$	−7.90704	−0.965999	−0.483000	+	0.875621i	$0.660453\pi$
$68$	−1.49307	−0.181062
$69$	0.00373868	0.000450084 0
$70$	1.93380	0.231133
$71$	−7.53708	−0.894487	−0.447244	−	0.894412i	$-0.647594\pi$
$71$	−7.53708	−0.894487	−0.447244	+	0.894412i	$0.647594\pi$
$72$	2.99989	0.353540
$73$	−9.66738	−1.13148	−0.565741	−	0.824583i	$-0.691410\pi$
$73$	−9.66738	−1.13148	−0.565741	+	0.824583i	$0.691410\pi$
$74$	0.851075	0.0989354
$75$	0.0380700	0.00439594
$76$	1.43647	0.164774
$77$	−4.10855	−0.468212
$78$	0.0705420	0.00798730
$79$	15.2302	1.71353	0.856767	−	0.515703i	$-0.172469\pi$
$79$	15.2302	1.71353	0.856767	+	0.515703i	$0.172469\pi$
$80$	−1.19509	−0.133615
$81$	8.99898	0.999886
$82$	−2.50850	−0.277018
$83$	−1.88445	−0.206845	−0.103423	−	0.994637i	$-0.532979\pi$
$83$	−1.88445	−0.206845	−0.103423	+	0.994637i	$0.532979\pi$
$84$	−0.0172469	−0.00188179
$85$	1.78436	0.193541
$86$	−7.23779	−0.780471
$87$	−0.0205667	−0.00220499
$88$	2.53909	0.270668
$89$	−10.1245	−1.07319	−0.536596	−	0.843839i	$-0.680290\pi$
$89$	−10.1245	−1.07319	−0.536596	+	0.843839i	$0.680290\pi$
$90$	−3.58514	−0.377907
$91$	10.7092	1.12263
$92$	−0.350766	−0.0365699
$93$	0.0722615	0.00749317
$94$	2.38199	0.245683
$95$	−1.71671	−0.176131
$96$	0.0106586	0.00108784
$97$	7.33946	0.745210	0.372605	−	0.927990i	$-0.378465\pi$
$97$	7.33946	0.745210	0.372605	+	0.927990i	$0.378465\pi$
$98$	4.38170	0.442618
$99$	7.61698	0.765536
$100$	−3.57176	−0.357176
$101$	−9.75708	−0.970866	−0.485433	−	0.874274i	$-0.661338\pi$
$101$	−9.75708	−0.970866	−0.485433	+	0.874274i	$0.661338\pi$
$102$	−0.0159141	−0.00157573
$103$	2.97170	0.292810	0.146405	−	0.989225i	$-0.453230\pi$
$103$	2.97170	0.292810	0.146405	+	0.989225i	$0.453230\pi$
$104$	−6.61830	−0.648978
$105$	0.0206116	0.00201149
$106$	5.21338	0.506368
$107$	0.466778	0.0451252	0.0225626	−	0.999745i	$-0.492817\pi$
$107$	0.466778	0.0451252	0.0225626	+	0.999745i	$0.492817\pi$
$108$	0.0639505	0.00615364
$109$	−11.4913	−1.10067	−0.550334	−	0.834945i	$-0.685499\pi$
$109$	−11.4913	−1.10067	−0.550334	+	0.834945i	$0.685499\pi$
$110$	−3.03444	−0.289323
$111$	0.00907128	0.000861008 0
$112$	1.61812	0.152898
$113$	−9.74852	−0.917063	−0.458532	−	0.888678i	$-0.651624\pi$
$113$	−9.74852	−0.917063	−0.458532	+	0.888678i	$0.651624\pi$
$114$	0.0153108	0.00143399
$115$	0.419197	0.0390903
$116$	1.92959	0.179158
$117$	−19.8542	−1.83552
$118$	−8.44227	−0.777174
$119$	−2.41597	−0.221471
$120$	−0.0127380	−0.00116282
$121$	−4.55302	−0.413911
$122$	−12.5641	−1.13750
$123$	−0.0267372	−0.00241081
$124$	−6.77963	−0.608829
$125$	10.2440	0.916254
$126$	4.85417	0.432444
$127$	−17.4266	−1.54636	−0.773179	−	0.634188i	$-0.781334\pi$
$127$	−17.4266	−1.54636	−0.773179	+	0.634188i	$0.781334\pi$
$128$	−1.00000	−0.0883883
$129$	−0.0771449	−0.00679223
$130$	7.90948	0.693707
$131$	−8.33703	−0.728410	−0.364205	−	0.931319i	$-0.618659\pi$
$131$	−8.33703	−0.728410	−0.364205	+	0.931319i	$0.618659\pi$
$132$	0.0270632	0.00235555
$133$	2.32438	0.201549
$134$	7.90704	0.683065
$135$	−0.0764266	−0.00657776
$136$	1.49307	0.128030
$137$	−15.2895	−1.30627	−0.653137	−	0.757240i	$-0.726547\pi$
$137$	−15.2895	−1.30627	−0.653137	+	0.757240i	$0.726547\pi$
$138$	−0.00373868	−0.000318257 0
$139$	−16.1548	−1.37023	−0.685116	−	0.728434i	$-0.740248\pi$
$139$	−16.1548	−1.37023	−0.685116	+	0.728434i	$0.740248\pi$
$140$	−1.93380	−0.163436
$141$	0.0253887	0.00213811
$142$	7.53708	0.632498
$143$	−16.8045	−1.40526
$144$	−2.99989	−0.249991
$145$	−2.30603	−0.191506
$146$	9.66738	0.800078
$147$	0.0467028	0.00385198
$148$	−0.851075	−0.0699579
$149$	13.2422	1.08484	0.542422	−	0.840106i	$-0.317507\pi$
$149$	13.2422	1.08484	0.542422	+	0.840106i	$0.317507\pi$
$150$	−0.0380700	−0.00310840
$151$	9.32092	0.758526	0.379263	−	0.925289i	$-0.376178\pi$
$151$	9.32092	0.758526	0.379263	+	0.925289i	$0.376178\pi$
$152$	−1.43647	−0.116513
$153$	4.47905	0.362109
$154$	4.10855	0.331076
$155$	8.10227	0.650790
$156$	−0.0705420	−0.00564788
$157$	5.73817	0.457956	0.228978	−	0.973432i	$-0.426462\pi$
$157$	5.73817	0.457956	0.228978	+	0.973432i	$0.426462\pi$
$158$	−15.2302	−1.21165
$159$	0.0555674	0.00440678
$160$	1.19509	0.0944802
$161$	−0.567580	−0.0447316
$162$	−8.99898	−0.707026
$163$	−14.1266	−1.10648	−0.553242	−	0.833021i	$-0.686609\pi$
$163$	−14.1266	−1.10648	−0.553242	+	0.833021i	$0.686609\pi$
$164$	2.50850	0.195881
$165$	−0.0323430	−0.00251790
$166$	1.88445	0.146262
$167$	−1.91689	−0.148334	−0.0741669	−	0.997246i	$-0.523630\pi$
$167$	−1.91689	−0.148334	−0.0741669	+	0.997246i	$0.523630\pi$
$168$	0.0172469	0.00133063
$169$	30.8020	2.36938
$170$	−1.78436	−0.136854
$171$	−4.30924	−0.329536
$172$	7.23779	0.551877
$173$	14.4272	1.09688	0.548438	−	0.836191i	$-0.315223\pi$
$173$	14.4272	1.09688	0.548438	+	0.836191i	$0.315223\pi$
$174$	0.0205667	0.00155916
$175$	−5.77952	−0.436891
$176$	−2.53909	−0.191391
$177$	−0.0899829	−0.00676353
$178$	10.1245	0.758861
$179$	0.775727	0.0579806	0.0289903	−	0.999580i	$-0.490771\pi$
$179$	0.775727	0.0579806	0.0289903	+	0.999580i	$0.490771\pi$
$180$	3.58514	0.267220
$181$	2.79910	0.208056	0.104028	−	0.994574i	$-0.466827\pi$
$181$	2.79910	0.208056	0.104028	+	0.994574i	$0.466827\pi$
$182$	−10.7092	−0.793818
$183$	−0.133916	−0.00989933
$184$	0.350766	0.0258588
$185$	1.01711	0.0747796
$186$	−0.0722615	−0.00529847
$187$	3.79105	0.277229
$188$	−2.38199	−0.173724
$189$	0.103479	0.00752702
$190$	1.71671	0.124543
$191$	−10.9693	−0.793713	−0.396856	−	0.917881i	$-0.629899\pi$
$191$	−10.9693	−0.793713	−0.396856	+	0.917881i	$0.629899\pi$
$192$	−0.0106586	−0.000769219 0
$193$	−12.8916	−0.927957	−0.463978	−	0.885847i	$-0.653578\pi$
$193$	−12.8916	−0.927957	−0.463978	+	0.885847i	$0.653578\pi$
$194$	−7.33946	−0.526943
$195$	0.0843041	0.00603714
$196$	−4.38170	−0.312978
$197$	−5.90721	−0.420871	−0.210436	−	0.977608i	$-0.567488\pi$
$197$	−5.90721	−0.420871	−0.210436	+	0.977608i	$0.567488\pi$
$198$	−7.61698	−0.541315
$199$	7.98531	0.566064	0.283032	−	0.959111i	$-0.408660\pi$
$199$	7.98531	0.566064	0.283032	+	0.959111i	$0.408660\pi$
$200$	3.57176	0.252561
$201$	0.0842781	0.00594452
$202$	9.75708	0.686506
$203$	3.12230	0.219142
$204$	0.0159141	0.00111421
$205$	−2.99789	−0.209382
$206$	−2.97170	−0.207048
$207$	1.05226	0.0731369
$208$	6.61830	0.458897
$209$	−3.64733	−0.252291
$210$	−0.0206116	−0.00142234
$211$	4.12247	0.283802	0.141901	−	0.989881i	$-0.454678\pi$
$211$	4.12247	0.283802	0.141901	+	0.989881i	$0.454678\pi$
$212$	−5.21338	−0.358056
$213$	0.0803349	0.00550445
$214$	−0.466778	−0.0319083
$215$	−8.64982	−0.589913
$216$	−0.0639505	−0.00435128
$217$	−10.9702	−0.744708
$218$	11.4913	0.778289
$219$	0.103041	0.00696286
$220$	3.03444	0.204582
$221$	−9.88161	−0.664709
$222$	−0.00907128	−0.000608824 0
$223$	26.4151	1.76889	0.884443	−	0.466648i	$-0.154538\pi$
$223$	26.4151	1.76889	0.884443	+	0.466648i	$0.154538\pi$
$224$	−1.61812	−0.108115
$225$	10.7149	0.714324
$226$	9.74852	0.648462
$227$	−24.7298	−1.64137	−0.820686	−	0.571380i	$-0.806408\pi$
$227$	−24.7298	−1.64137	−0.820686	+	0.571380i	$0.806408\pi$
$228$	−0.0153108	−0.00101398
$229$	23.1209	1.52787	0.763935	−	0.645294i	$-0.223265\pi$
$229$	23.1209	1.52787	0.763935	+	0.645294i	$0.223265\pi$
$230$	−0.419197	−0.0276410
$231$	0.0437914	0.00288126
$232$	−1.92959	−0.126684
$233$	−18.9023	−1.23833	−0.619164	−	0.785262i	$-0.712528\pi$
$233$	−18.9023	−1.23833	−0.619164	+	0.785262i	$0.712528\pi$
$234$	19.8542	1.29791
$235$	2.84669	0.185698
$236$	8.44227	0.549545
$237$	−0.162333	−0.0105447
$238$	2.41597	0.156604
$239$	−16.7805	−1.08544	−0.542719	−	0.839915i	$-0.682605\pi$
$239$	−16.7805	−1.08544	−0.542719	+	0.839915i	$0.682605\pi$
$240$	0.0127380	0.000822235 0
$241$	−28.3703	−1.82749	−0.913747	−	0.406284i	$-0.866824\pi$
$241$	−28.3703	−1.82749	−0.913747	+	0.406284i	$0.866824\pi$
$242$	4.55302	0.292679
$243$	−0.287768	−0.0184603
$244$	12.5641	0.804332
$245$	5.23653	0.334549
$246$	0.0267372	0.00170470
$247$	9.50699	0.604915
$248$	6.77963	0.430507
$249$	0.0200856	0.00127288
$250$	−10.2440	−0.647889
$251$	−21.2740	−1.34280	−0.671400	−	0.741095i	$-0.734307\pi$
$251$	−21.2740	−1.34280	−0.671400	+	0.741095i	$0.734307\pi$
$252$	−4.85417	−0.305784
$253$	0.890626	0.0559932
$254$	17.4266	1.09344
$255$	−0.0190188	−0.00119100
$256$	1.00000	0.0625000
$257$	−12.6062	−0.786356	−0.393178	−	0.919462i	$-0.628624\pi$
$257$	−12.6062	−0.786356	−0.393178	+	0.919462i	$0.628624\pi$
$258$	0.0771449	0.00480283
$259$	−1.37714	−0.0855713
$260$	−7.90948	−0.490525
$261$	−5.78854	−0.358302
$262$	8.33703	0.515063
$263$	−28.8178	−1.77698	−0.888490	−	0.458896i	$-0.848245\pi$
$263$	−28.8178	−1.77698	−0.888490	+	0.458896i	$0.848245\pi$
$264$	−0.0270632	−0.00166562
$265$	6.23046	0.382734
$266$	−2.32438	−0.142517
$267$	0.107913	0.00660416
$268$	−7.90704	−0.483000
$269$	19.1005	1.16458	0.582290	−	0.812981i	$-0.302157\pi$
$269$	19.1005	1.16458	0.582290	+	0.812981i	$0.302157\pi$
$270$	0.0764266	0.00465118
$271$	−11.5287	−0.700318	−0.350159	−	0.936690i	$-0.613872\pi$
$271$	−11.5287	−0.700318	−0.350159	+	0.936690i	$0.613872\pi$
$272$	−1.49307	−0.0905308
$273$	−0.114145	−0.00690838
$274$	15.2895	0.923675
$275$	9.06902	0.546882
$276$	0.00373868	0.000225042 0
$277$	20.2989	1.21964	0.609820	−	0.792540i	$-0.291242\pi$
$277$	20.2989	1.21964	0.609820	+	0.792540i	$0.291242\pi$
$278$	16.1548	0.968900
$279$	20.3381	1.21761
$280$	1.93380	0.115566
$281$	−14.7212	−0.878192	−0.439096	−	0.898440i	$-0.644701\pi$
$281$	−14.7212	−0.878192	−0.439096	+	0.898440i	$0.644701\pi$
$282$	−0.0253887	−0.00151188
$283$	4.65096	0.276471	0.138235	−	0.990399i	$-0.455857\pi$
$283$	4.65096	0.276471	0.138235	+	0.990399i	$0.455857\pi$
$284$	−7.53708	−0.447244
$285$	0.0182978	0.00108387
$286$	16.8045	0.993669
$287$	4.05905	0.239598
$288$	2.99989	0.176770
$289$	−14.7707	−0.868867
$290$	2.30603	0.135415
$291$	−0.0782285	−0.00458584
$292$	−9.66738	−0.565741
$293$	−7.14585	−0.417465	−0.208733	−	0.977973i	$-0.566934\pi$
$293$	−7.14585	−0.417465	−0.208733	+	0.977973i	$0.566934\pi$
$294$	−0.0467028	−0.00272376
$295$	−10.0893	−0.587420
$296$	0.851075	0.0494677
$297$	−0.162376	−0.00942202
$298$	−13.2422	−0.767101
$299$	−2.32147	−0.134254
$300$	0.0380700	0.00219797
$301$	11.7116	0.675045
$302$	−9.32092	−0.536359
$303$	0.103997	0.00597447
$304$	1.43647	0.0823871
$305$	−15.0152	−0.859768
$306$	−4.47905	−0.256050
$307$	−15.7961	−0.901531	−0.450766	−	0.892642i	$-0.648849\pi$
$307$	−15.7961	−0.901531	−0.450766	+	0.892642i	$0.648849\pi$
$308$	−4.10855	−0.234106
$309$	−0.0316742	−0.00180188
$310$	−8.10227	−0.460178
$311$	−1.45358	−0.0824251	−0.0412126	−	0.999150i	$-0.513122\pi$
$311$	−1.45358	−0.0824251	−0.0412126	+	0.999150i	$0.513122\pi$
$312$	0.0705420	0.00399365
$313$	−11.6433	−0.658118	−0.329059	−	0.944309i	$-0.606732\pi$
$313$	−11.6433	−0.658118	−0.329059	+	0.944309i	$0.606732\pi$
$314$	−5.73817	−0.323824
$315$	5.80117	0.326859
$316$	15.2302	0.856767
$317$	−24.6616	−1.38513	−0.692566	−	0.721355i	$-0.743520\pi$
$317$	−24.6616	−1.38513	−0.692566	+	0.721355i	$0.743520\pi$
$318$	−0.0555674	−0.00311606
$319$	−4.89940	−0.274314
$320$	−1.19509	−0.0668076
$321$	−0.00497521	−0.000277689 0
$322$	0.567580	0.0316300
$323$	−2.14475	−0.119337
$324$	8.99898	0.499943
$325$	−23.6390	−1.31125
$326$	14.1266	0.782402
$327$	0.122481	0.00677323
$328$	−2.50850	−0.138509
$329$	−3.85434	−0.212496
$330$	0.0323430	0.00178042
$331$	13.0553	0.717582	0.358791	−	0.933418i	$-0.383189\pi$
$331$	13.0553	0.717582	0.358791	+	0.933418i	$0.383189\pi$
$332$	−1.88445	−0.103423
$333$	2.55313	0.139911
$334$	1.91689	0.104888
$335$	9.44964	0.516289
$336$	−0.0172469	−0.000940895 0
$337$	−11.0640	−0.602692	−0.301346	−	0.953515i	$-0.597436\pi$
$337$	−11.0640	−0.602692	−0.301346	+	0.953515i	$0.597436\pi$
$338$	−30.8020	−1.67541
$339$	0.103906	0.00564338
$340$	1.78436	0.0967703
$341$	17.2141	0.932196
$342$	4.30924	0.233017
$343$	−18.4169	−0.994420
$344$	−7.23779	−0.390236
$345$	−0.00446806	−0.000240552 0
$346$	−14.4272	−0.775609
$347$	15.8355	0.850096	0.425048	−	0.905171i	$-0.360257\pi$
$347$	15.8355	0.850096	0.425048	+	0.905171i	$0.360257\pi$
$348$	−0.0205667	−0.00110249
$349$	−24.8012	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$349$	−24.8012	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$350$	5.77952	0.308929
$351$	0.423244	0.0225911
$352$	2.53909	0.135334
$353$	8.62165	0.458884	0.229442	−	0.973322i	$-0.426310\pi$
$353$	8.62165	0.458884	0.229442	+	0.973322i	$0.426310\pi$
$354$	0.0899829	0.00478254
$355$	9.00750	0.478068
$356$	−10.1245	−0.536596
$357$	0.0257508	0.00136288
$358$	−0.775727	−0.0409984
$359$	32.4158	1.71084	0.855420	−	0.517936i	$-0.173299\pi$
$359$	32.4158	1.71084	0.855420	+	0.517936i	$0.173299\pi$
$360$	−3.58514	−0.188953
$361$	−16.9366	−0.891398
$362$	−2.79910	−0.147118
$363$	0.0485289	0.00254711
$364$	10.7092	0.561314
$365$	11.5534	0.604732
$366$	0.133916	0.00699988
$367$	13.7079	0.715548	0.357774	−	0.933808i	$-0.383536\pi$
$367$	13.7079	0.715548	0.357774	+	0.933808i	$0.383536\pi$
$368$	−0.350766	−0.0182849
$369$	−7.52522	−0.391747
$370$	−1.01711	−0.0528771
$371$	−8.43585	−0.437968
$372$	0.0722615	0.00374658
$373$	−19.1435	−0.991212	−0.495606	−	0.868547i	$-0.665054\pi$
$373$	−19.1435	−0.991212	−0.495606	+	0.868547i	$0.665054\pi$
$374$	−3.79105	−0.196030
$375$	−0.109187	−0.00563840
$376$	2.38199	0.122842
$377$	12.7706	0.657719
$378$	−0.103479	−0.00532241
$379$	−14.8823	−0.764454	−0.382227	−	0.924068i	$-0.624843\pi$
$379$	−14.8823	−0.764454	−0.382227	+	0.924068i	$0.624843\pi$
$380$	−1.71671	−0.0880654
$381$	0.185743	0.00951590
$382$	10.9693	0.561240
$383$	−1.70493	−0.0871180	−0.0435590	−	0.999051i	$-0.513870\pi$
$383$	−1.70493	−0.0871180	−0.0435590	+	0.999051i	$0.513870\pi$
$384$	0.0106586	0.000543920 0
$385$	4.91009	0.250241
$386$	12.8916	0.656164
$387$	−21.7126	−1.10371
$388$	7.33946	0.372605
$389$	−29.9178	−1.51689	−0.758446	−	0.651736i	$-0.774041\pi$
$389$	−29.9178	−1.51689	−0.758446	+	0.651736i	$0.774041\pi$
$390$	−0.0843041	−0.00426890
$391$	0.523719	0.0264856
$392$	4.38170	0.221309
$393$	0.0888612	0.00448245
$394$	5.90721	0.297601
$395$	−18.2015	−0.915817
$396$	7.61698	0.382768
$397$	26.8043	1.34527	0.672635	−	0.739974i	$-0.265162\pi$
$397$	26.8043	1.34527	0.672635	+	0.739974i	$0.265162\pi$
$398$	−7.98531	−0.400268
$399$	−0.0247746	−0.00124028
$400$	−3.57176	−0.178588
$401$	11.1295	0.555781	0.277891	−	0.960613i	$-0.410365\pi$
$401$	11.1295	0.555781	0.277891	+	0.960613i	$0.410365\pi$
$402$	−0.0842781	−0.00420341
$403$	−44.8697	−2.23512
$404$	−9.75708	−0.485433
$405$	−10.7546	−0.534400
$406$	−3.12230	−0.154957
$407$	2.16096	0.107115
$408$	−0.0159141	−0.000787864 0
$409$	−9.25102	−0.457434	−0.228717	−	0.973493i	$-0.573453\pi$
$409$	−9.25102	−0.457434	−0.228717	+	0.973493i	$0.573453\pi$
$410$	2.99789	0.148055
$411$	0.162965	0.00803849
$412$	2.97170	0.146405
$413$	13.6606	0.672193
$414$	−1.05226	−0.0517156
$415$	2.25209	0.110551
$416$	−6.61830	−0.324489
$417$	0.172188	0.00843207
$418$	3.64733	0.178397
$419$	−13.7122	−0.669885	−0.334943	−	0.942239i	$-0.608717\pi$
$419$	−13.7122	−0.669885	−0.334943	+	0.942239i	$0.608717\pi$
$420$	0.0206116	0.00100574
$421$	−12.4715	−0.607823	−0.303911	−	0.952700i	$-0.598293\pi$
$421$	−12.4715	−0.607823	−0.303911	+	0.952700i	$0.598293\pi$
$422$	−4.12247	−0.200679
$423$	7.14570	0.347436
$424$	5.21338	0.253184
$425$	5.33289	0.258683
$426$	−0.0803349	−0.00389224
$427$	20.3301	0.983845
$428$	0.466778	0.0225626
$429$	0.179112	0.00864763
$430$	8.64982	0.417131
$431$	−12.6963	−0.611560	−0.305780	−	0.952102i	$-0.598917\pi$
$431$	−12.6963	−0.611560	−0.305780	+	0.952102i	$0.598917\pi$
$432$	0.0639505	0.00307682
$433$	31.3752	1.50780	0.753898	−	0.656991i	$-0.228171\pi$
$433$	31.3752	1.50780	0.753898	+	0.656991i	$0.228171\pi$
$434$	10.9702	0.526588
$435$	0.0245791	0.00117848
$436$	−11.4913	−0.550334
$437$	−0.503864	−0.0241031
$438$	−0.103041	−0.00492348
$439$	−12.5412	−0.598559	−0.299280	−	0.954165i	$-0.596746\pi$
$439$	−12.5412	−0.598559	−0.299280	+	0.954165i	$0.596746\pi$
$440$	−3.03444	−0.144661
$441$	13.1446	0.625933
$442$	9.88161	0.470020
$443$	6.44117	0.306029	0.153015	−	0.988224i	$-0.451102\pi$
$443$	6.44117	0.306029	0.153015	+	0.988224i	$0.451102\pi$
$444$	0.00907128	0.000430504 0
$445$	12.0997	0.573579
$446$	−26.4151	−1.25079
$447$	−0.141144	−0.00667586
$448$	1.61812	0.0764489
$449$	35.3339	1.66751	0.833755	−	0.552134i	$-0.186186\pi$
$449$	35.3339	1.66751	0.833755	+	0.552134i	$0.186186\pi$
$450$	−10.7149	−0.505104
$451$	−6.36931	−0.299919
$452$	−9.74852	−0.458532
$453$	−0.0993481	−0.00466778
$454$	24.7298	1.16062
$455$	−12.7985	−0.600001
$456$	0.0153108	0.000716993 0
$457$	−19.2302	−0.899551	−0.449775	−	0.893142i	$-0.648496\pi$
$457$	−19.2302	−0.899551	−0.449775	+	0.893142i	$0.648496\pi$
$458$	−23.1209	−1.08037
$459$	−0.0954827	−0.00445675
$460$	0.419197	0.0195452
$461$	8.28130	0.385699	0.192849	−	0.981228i	$-0.438227\pi$
$461$	8.28130	0.385699	0.192849	+	0.981228i	$0.438227\pi$
$462$	−0.0437914	−0.00203736
$463$	−26.4724	−1.23028	−0.615139	−	0.788419i	$-0.710900\pi$
$463$	−26.4724	−1.23028	−0.615139	+	0.788419i	$0.710900\pi$
$464$	1.92959	0.0895789
$465$	−0.0863590	−0.00400480
$466$	18.9023	0.875630
$467$	22.9936	1.06402	0.532009	−	0.846739i	$-0.321437\pi$
$467$	22.9936	1.06402	0.532009	+	0.846739i	$0.321437\pi$
$468$	−19.8542	−0.917759
$469$	−12.7945	−0.590796
$470$	−2.84669	−0.131308
$471$	−0.0611610	−0.00281815
$472$	−8.44227	−0.388587
$473$	−18.3774	−0.844994
$474$	0.162333	0.00745621
$475$	−5.13072	−0.235414
$476$	−2.41597	−0.110736
$477$	15.6395	0.716085
$478$	16.7805	0.767520
$479$	2.41181	0.110198	0.0550992	−	0.998481i	$-0.482452\pi$
$479$	2.41181	0.110198	0.0550992	+	0.998481i	$0.482452\pi$
$480$	−0.0127380	−0.000581408 0
$481$	−5.63267	−0.256828
$482$	28.3703	1.29223
$483$	0.00604962	0.000275267 0
$484$	−4.55302	−0.206955
$485$	−8.77133	−0.398285
$486$	0.287768	0.0130534
$487$	−7.66671	−0.347412	−0.173706	−	0.984798i	$-0.555574\pi$
$487$	−7.66671	−0.347412	−0.173706	+	0.984798i	$0.555574\pi$
$488$	−12.5641	−0.568749
$489$	0.150570	0.00680903
$490$	−5.23653	−0.236562
$491$	−4.83529	−0.218214	−0.109107	−	0.994030i	$-0.534799\pi$
$491$	−4.83529	−0.218214	−0.109107	+	0.994030i	$0.534799\pi$
$492$	−0.0267372	−0.00120540
$493$	−2.88101	−0.129754
$494$	−9.50699	−0.427740
$495$	−9.10299	−0.409149
$496$	−6.77963	−0.304414
$497$	−12.1959	−0.547060
$498$	−0.0200856	−0.000900059 0
$499$	−34.8875	−1.56178	−0.780888	−	0.624670i	$-0.785233\pi$
$499$	−34.8875	−1.56178	−0.780888	+	0.624670i	$0.785233\pi$
$500$	10.2440	0.458127
$501$	0.0204314	0.000912809 0
$502$	21.2740	0.949503
$503$	29.1385	1.29922	0.649610	−	0.760268i	$-0.274932\pi$
$503$	29.1385	1.29922	0.649610	+	0.760268i	$0.274932\pi$
$504$	4.85417	0.216222
$505$	11.6606	0.518890
$506$	−0.890626	−0.0395932
$507$	−0.328306	−0.0145806
$508$	−17.4266	−0.773179
$509$	−4.34483	−0.192581	−0.0962905	−	0.995353i	$-0.530698\pi$
$509$	−4.34483	−0.192581	−0.0962905	+	0.995353i	$0.530698\pi$
$510$	0.0190188	0.000842165 0
$511$	−15.6430	−0.692004
$512$	−1.00000	−0.0441942
$513$	0.0918629	0.00405585
$514$	12.6062	0.556038
$515$	−3.55145	−0.156495
$516$	−0.0771449	−0.00339611
$517$	6.04809	0.265994
$518$	1.37714	0.0605080
$519$	−0.153774	−0.00674991
$520$	7.90948	0.346853
$521$	4.59485	0.201304	0.100652	−	0.994922i	$-0.467907\pi$
$521$	4.59485	0.201304	0.100652	+	0.994922i	$0.467907\pi$
$522$	5.78854	0.253358
$523$	1.83579	0.0802736	0.0401368	−	0.999194i	$-0.487221\pi$
$523$	1.83579	0.0802736	0.0401368	+	0.999194i	$0.487221\pi$
$524$	−8.33703	−0.364205
$525$	0.0616017	0.00268852
$526$	28.8178	1.25651
$527$	10.1225	0.440942
$528$	0.0270632	0.00117777
$529$	−22.8770	−0.994651
$530$	−6.23046	−0.270634
$531$	−25.3258	−1.09905
$532$	2.32438	0.100774
$533$	16.6020	0.719114
$534$	−0.107913	−0.00466985
$535$	−0.557842	−0.0241176
$536$	7.90704	0.341532
$537$	−0.00826817	−0.000356798 0
$538$	−19.1005	−0.823483
$539$	11.1255	0.479210
$540$	−0.0764266	−0.00328888
$541$	−6.10478	−0.262465	−0.131232	−	0.991352i	$-0.541893\pi$
$541$	−6.10478	−0.262465	−0.131232	+	0.991352i	$0.541893\pi$
$542$	11.5287	0.495200
$543$	−0.0298346	−0.00128032
$544$	1.49307	0.0640149
$545$	13.7331	0.588263
$546$	0.114145	0.00488496
$547$	−2.58246	−0.110418	−0.0552091	−	0.998475i	$-0.517583\pi$
$547$	−2.58246	−0.110418	−0.0552091	+	0.998475i	$0.517583\pi$
$548$	−15.2895	−0.653137
$549$	−37.6908	−1.60860
$550$	−9.06902	−0.386704
$551$	2.77179	0.118082
$552$	−0.00373868	−0.000159129 0
$553$	24.6443	1.04798
$554$	−20.2989	−0.862416
$555$	−0.0108410	−0.000460175 0
$556$	−16.1548	−0.685116
$557$	−12.2326	−0.518314	−0.259157	−	0.965835i	$-0.583445\pi$
$557$	−12.2326	−0.518314	−0.259157	+	0.965835i	$0.583445\pi$
$558$	−20.3381	−0.860981
$559$	47.9019	2.02604
$560$	−1.93380	−0.0817179
$561$	−0.0404073	−0.00170600
$562$	14.7212	0.620976
$563$	15.7733	0.664766	0.332383	−	0.943145i	$-0.392147\pi$
$563$	15.7733	0.664766	0.332383	+	0.943145i	$0.392147\pi$
$564$	0.0253887	0.00106906
$565$	11.6504	0.490135
$566$	−4.65096	−0.195494
$567$	14.5614	0.611521
$568$	7.53708	0.316249
$569$	−14.3651	−0.602215	−0.301107	−	0.953590i	$-0.597356\pi$
$569$	−14.3651	−0.602215	−0.301107	+	0.953590i	$0.597356\pi$
$570$	−0.0182978	−0.000766409 0
$571$	13.2734	0.555473	0.277737	−	0.960657i	$-0.410416\pi$
$571$	13.2734	0.555473	0.277737	+	0.960657i	$0.410416\pi$
$572$	−16.8045	−0.702630
$573$	0.116918	0.00488431
$574$	−4.05905	−0.169422
$575$	1.25285	0.0522475
$576$	−2.99989	−0.124995
$577$	−17.4865	−0.727971	−0.363985	−	0.931405i	$-0.618584\pi$
$577$	−17.4865	−0.727971	−0.363985	+	0.931405i	$0.618584\pi$
$578$	14.7707	0.614382
$579$	0.137406	0.00571042
$580$	−2.30603	−0.0957528
$581$	−3.04926	−0.126505
$582$	0.0782285	0.00324268
$583$	13.2372	0.548230
$584$	9.66738	0.400039
$585$	23.7275	0.981013
$586$	7.14585	0.295192
$587$	21.7033	0.895792	0.447896	−	0.894086i	$-0.352173\pi$
$587$	21.7033	0.895792	0.447896	+	0.894086i	$0.352173\pi$
$588$	0.0467028	0.00192599
$589$	−9.73873	−0.401277
$590$	10.0893	0.415369
$591$	0.0629627	0.00258994
$592$	−0.851075	−0.0349790
$593$	17.4700	0.717408	0.358704	−	0.933451i	$-0.383219\pi$
$593$	17.4700	0.717408	0.358704	+	0.933451i	$0.383219\pi$
$594$	0.162376	0.00666237
$595$	2.88730	0.118368
$596$	13.2422	0.542422
$597$	−0.0851124	−0.00348342
$598$	2.32147	0.0949322
$599$	7.07583	0.289111	0.144555	−	0.989497i	$-0.453825\pi$
$599$	7.07583	0.289111	0.144555	+	0.989497i	$0.453825\pi$
$600$	−0.0380700	−0.00155420
$601$	8.00512	0.326536	0.163268	−	0.986582i	$-0.447797\pi$
$601$	8.00512	0.326536	0.163268	+	0.986582i	$0.447797\pi$
$602$	−11.7116	−0.477329
$603$	23.7202	0.965963
$604$	9.32092	0.379263
$605$	5.44127	0.221219
$606$	−0.103997	−0.00422459
$607$	24.4223	0.991272	0.495636	−	0.868530i	$-0.334935\pi$
$607$	24.4223	0.991272	0.495636	+	0.868530i	$0.334935\pi$
$608$	−1.43647	−0.0582565
$609$	−0.0332794	−0.00134855
$610$	15.0152	0.607948
$611$	−15.7647	−0.637773
$612$	4.47905	0.181055
$613$	−2.02552	−0.0818100	−0.0409050	−	0.999163i	$-0.513024\pi$
$613$	−2.02552	−0.0818100	−0.0409050	+	0.999163i	$0.513024\pi$
$614$	15.7961	0.637479
$615$	0.0319533	0.00128848
$616$	4.10855	0.165538
$617$	−38.0980	−1.53377	−0.766885	−	0.641785i	$-0.778194\pi$
$617$	−38.0980	−1.53377	−0.766885	+	0.641785i	$0.778194\pi$
$618$	0.0316742	0.00127412
$619$	23.7989	0.956559	0.478280	−	0.878208i	$-0.341261\pi$
$619$	23.7989	0.956559	0.478280	+	0.878208i	$0.341261\pi$
$620$	8.10227	0.325395
$621$	−0.0224316	−0.000900151 0
$622$	1.45358	0.0582834
$623$	−16.3826	−0.656354
$624$	−0.0705420	−0.00282394
$625$	5.61624	0.224650
$626$	11.6433	0.465360
$627$	0.0388754	0.00155254
$628$	5.73817	0.228978
$629$	1.27072	0.0506668
$630$	−5.80117	−0.231124
$631$	26.4302	1.05217	0.526085	−	0.850432i	$-0.323659\pi$
$631$	26.4302	1.05217	0.526085	+	0.850432i	$0.323659\pi$
$632$	−15.2302	−0.605826
$633$	−0.0439398	−0.00174645
$634$	24.6616	0.979436
$635$	20.8263	0.826468
$636$	0.0555674	0.00220339
$637$	−28.9994	−1.14900
$638$	4.89940	0.193969
$639$	22.6104	0.894453
$640$	1.19509	0.0472401
$641$	−27.6999	−1.09408	−0.547040	−	0.837107i	$-0.684245\pi$
$641$	−27.6999	−1.09408	−0.547040	+	0.837107i	$0.684245\pi$
$642$	0.00497521	0.000196356 0
$643$	−37.0275	−1.46022	−0.730110	−	0.683329i	$-0.760531\pi$
$643$	−37.0275	−1.46022	−0.730110	+	0.683329i	$0.760531\pi$
$644$	−0.567580	−0.0223658
$645$	0.0921951	0.00363018
$646$	2.14475	0.0843841
$647$	13.6338	0.535998	0.267999	−	0.963419i	$-0.413638\pi$
$647$	13.6338	0.535998	0.267999	+	0.963419i	$0.413638\pi$
$648$	−8.99898	−0.353513
$649$	−21.4357	−0.841424
$650$	23.6390	0.927197
$651$	0.116928	0.00458275
$652$	−14.1266	−0.553242
$653$	−32.2144	−1.26065	−0.630323	−	0.776333i	$-0.717077\pi$
$653$	−32.2144	−1.26065	−0.630323	+	0.776333i	$0.717077\pi$
$654$	−0.122481	−0.00478940
$655$	9.96351	0.389306
$656$	2.50850	0.0979406
$657$	29.0010	1.13144
$658$	3.85434	0.150258
$659$	20.7910	0.809904	0.404952	−	0.914338i	$-0.367288\pi$
$659$	20.7910	0.809904	0.404952	+	0.914338i	$0.367288\pi$
$660$	−0.0323430	−0.00125895
$661$	23.7832	0.925061	0.462531	−	0.886603i	$-0.346942\pi$
$661$	23.7832	0.925061	0.462531	+	0.886603i	$0.346942\pi$
$662$	−13.0553	−0.507407
$663$	0.105324	0.00409045
$664$	1.88445	0.0731309
$665$	−2.77784	−0.107720
$666$	−2.55313	−0.0989317
$667$	−0.676833	−0.0262071
$668$	−1.91689	−0.0741669
$669$	−0.281548	−0.0108853
$670$	−9.44964	−0.365071
$671$	−31.9013	−1.23154
$672$	0.0172469	0.000665313 0
$673$	−1.44495	−0.0556988	−0.0278494	−	0.999612i	$-0.508866\pi$
$673$	−1.44495	−0.0556988	−0.0278494	+	0.999612i	$0.508866\pi$
$674$	11.0640	0.426168
$675$	−0.228416	−0.00879172
$676$	30.8020	1.18469
$677$	−8.96255	−0.344459	−0.172229	−	0.985057i	$-0.555097\pi$
$677$	−8.96255	−0.344459	−0.172229	+	0.985057i	$0.555097\pi$
$678$	−0.103906	−0.00399047
$679$	11.8761	0.455763
$680$	−1.78436	−0.0684270
$681$	0.263585	0.0101006
$682$	−17.2141	−0.659162
$683$	−9.20082	−0.352060	−0.176030	−	0.984385i	$-0.556326\pi$
$683$	−9.20082	−0.352060	−0.176030	+	0.984385i	$0.556326\pi$
$684$	−4.30924	−0.164768
$685$	18.2724	0.698152
$686$	18.4169	0.703161
$687$	−0.246436	−0.00940213
$688$	7.23779	0.275938
$689$	−34.5037	−1.31449
$690$	0.00446806	0.000170096 0
$691$	−29.8622	−1.13601	−0.568006	−	0.823024i	$-0.692285\pi$
$691$	−29.8622	−1.13601	−0.568006	+	0.823024i	$0.692285\pi$
$692$	14.4272	0.548438
$693$	12.3252	0.468195
$694$	−15.8355	−0.601109
$695$	19.3064	0.732335
$696$	0.0205667	0.000779580 0
$697$	−3.74537	−0.141866
$698$	24.8012	0.938737
$699$	0.201472	0.00762037
$700$	−5.77952	−0.218445
$701$	46.9456	1.77311	0.886555	−	0.462623i	$-0.153092\pi$
$701$	46.9456	1.77311	0.886555	+	0.462623i	$0.153092\pi$
$702$	−0.423244	−0.0159743
$703$	−1.22254	−0.0461091
$704$	−2.53909	−0.0956956
$705$	−0.0303418	−0.00114274
$706$	−8.62165	−0.324480
$707$	−15.7881	−0.593773
$708$	−0.0899829	−0.00338176
$709$	23.1958	0.871136	0.435568	−	0.900156i	$-0.356548\pi$
$709$	23.1958	0.871136	0.435568	+	0.900156i	$0.356548\pi$
$710$	−9.00750	−0.338045
$711$	−45.6890	−1.71347
$712$	10.1245	0.379431
$713$	2.37806	0.0890591
$714$	−0.0257508	−0.000963701 0
$715$	20.0829	0.751057
$716$	0.775727	0.0289903
$717$	0.178856	0.00667952
$718$	−32.4158	−1.20975
$719$	−38.1932	−1.42436	−0.712182	−	0.701995i	$-0.752293\pi$
$719$	−38.1932	−1.42436	−0.712182	+	0.701995i	$0.752293\pi$
$720$	3.58514	0.133610
$721$	4.80855	0.179080
$722$	16.9366	0.630313
$723$	0.302388	0.0112459
$724$	2.79910	0.104028
$725$	−6.89202	−0.255963
$726$	−0.0485289	−0.00180108
$727$	3.91560	0.145222	0.0726108	−	0.997360i	$-0.476867\pi$
$727$	3.91560	0.145222	0.0726108	+	0.997360i	$0.476867\pi$
$728$	−10.7092	−0.396909
$729$	−26.9939	−0.999773
$730$	−11.5534	−0.427610
$731$	−10.8065	−0.399695
$732$	−0.133916	−0.00494966
$733$	−41.2911	−1.52512	−0.762561	−	0.646917i	$-0.776058\pi$
$733$	−41.2911	−1.52512	−0.762561	+	0.646917i	$0.776058\pi$
$734$	−13.7079	−0.505969
$735$	−0.0558141	−0.00205873
$736$	0.350766	0.0129294
$737$	20.0767	0.739535
$738$	7.52522	0.277007
$739$	28.2298	1.03845	0.519225	−	0.854638i	$-0.326221\pi$
$739$	28.2298	1.03845	0.519225	+	0.854638i	$0.326221\pi$
$740$	1.01711	0.0373898
$741$	−0.101331	−0.00372250
$742$	8.43585	0.309690
$743$	48.7604	1.78885	0.894424	−	0.447221i	$-0.147586\pi$
$743$	48.7604	1.78885	0.894424	+	0.447221i	$0.147586\pi$
$744$	−0.0722615	−0.00264923
$745$	−15.8256	−0.579807
$746$	19.1435	0.700893
$747$	5.65314	0.206838
$748$	3.79105	0.138614
$749$	0.755302	0.0275981
$750$	0.109187	0.00398695
$751$	−21.6317	−0.789350	−0.394675	−	0.918821i	$-0.629143\pi$
$751$	−21.6317	−0.789350	−0.394675	+	0.918821i	$0.629143\pi$
$752$	−2.38199	−0.0868622
$753$	0.226751	0.00826326
$754$	−12.7706	−0.465078
$755$	−11.1393	−0.405402
$756$	0.103479	0.00376351
$757$	16.1100	0.585529	0.292764	−	0.956185i	$-0.405425\pi$
$757$	16.1100	0.585529	0.292764	+	0.956185i	$0.405425\pi$
$758$	14.8823	0.540551
$759$	−0.00949284	−0.000344568 0
$760$	1.71671	0.0622717
$761$	42.0730	1.52514	0.762572	−	0.646904i	$-0.223936\pi$
$761$	42.0730	1.52514	0.762572	+	0.646904i	$0.223936\pi$
$762$	−0.185743	−0.00672876
$763$	−18.5943	−0.673158
$764$	−10.9693	−0.396856
$765$	−5.35287	−0.193533
$766$	1.70493	0.0616018
$767$	55.8735	2.01747
$768$	−0.0106586	−0.000384610 0
$769$	−40.7047	−1.46785	−0.733924	−	0.679231i	$-0.762313\pi$
$769$	−40.7047	−1.46785	−0.733924	+	0.679231i	$0.762313\pi$
$770$	−4.91009	−0.176947
$771$	0.134365	0.00483904
$772$	−12.8916	−0.463978
$773$	20.3446	0.731746	0.365873	−	0.930665i	$-0.380770\pi$
$773$	20.3446	0.731746	0.365873	+	0.930665i	$0.380770\pi$
$774$	21.7126	0.780442
$775$	24.2152	0.869836
$776$	−7.33946	−0.263471
$777$	0.0146784	0.000526584 0
$778$	29.9178	1.07261
$779$	3.60339	0.129105
$780$	0.0843041	0.00301857
$781$	19.1373	0.684788
$782$	−0.523719	−0.0187281
$783$	0.123398	0.00440989
$784$	−4.38170	−0.156489
$785$	−6.85764	−0.244760
$786$	−0.0888612	−0.00316957
$787$	22.0593	0.786331	0.393165	−	0.919468i	$-0.371380\pi$
$787$	22.0593	0.786331	0.393165	+	0.919468i	$0.371380\pi$
$788$	−5.90721	−0.210436
$789$	0.307158	0.0109351
$790$	18.2015	0.647581
$791$	−15.7742	−0.560868
$792$	−7.61698	−0.270658
$793$	83.1529	2.95284
$794$	−26.8043	−0.951250
$795$	−0.0664081	−0.00235525
$796$	7.98531	0.283032
$797$	7.65377	0.271111	0.135555	−	0.990770i	$-0.456718\pi$
$797$	7.65377	0.271111	0.135555	+	0.990770i	$0.456718\pi$
$798$	0.0247746	0.000877012 0
$799$	3.55648	0.125819
$800$	3.57176	0.126281
$801$	30.3723	1.07315
$802$	−11.1295	−0.392997
$803$	24.5464	0.866222
$804$	0.0842781	0.00297226
$805$	0.678310	0.0239073
$806$	44.8697	1.58047
$807$	−0.203585	−0.00716654
$808$	9.75708	0.343253
$809$	−15.4655	−0.543738	−0.271869	−	0.962334i	$-0.587642\pi$
$809$	−15.4655	−0.543738	−0.271869	+	0.962334i	$0.587642\pi$
$810$	10.7546	0.377878
$811$	15.5825	0.547176	0.273588	−	0.961847i	$-0.411790\pi$
$811$	15.5825	0.547176	0.273588	+	0.961847i	$0.411790\pi$
$812$	3.12230	0.109571
$813$	0.122880	0.00430958
$814$	−2.16096	−0.0757415
$815$	16.8826	0.591372
$816$	0.0159141	0.000557104 0
$817$	10.3969	0.363740
$818$	9.25102	0.323454
$819$	−32.1264	−1.12259
$820$	−2.99789	−0.104691
$821$	17.6274	0.615202	0.307601	−	0.951515i	$-0.400474\pi$
$821$	17.6274	0.615202	0.307601	+	0.951515i	$0.400474\pi$
$822$	−0.162965	−0.00568407
$823$	48.7883	1.70065	0.850326	−	0.526256i	$-0.176405\pi$
$823$	48.7883	1.70065	0.850326	+	0.526256i	$0.176405\pi$
$824$	−2.97170	−0.103524
$825$	−0.0966632	−0.00336538
$826$	−13.6606	−0.475312
$827$	22.6835	0.788782	0.394391	−	0.918943i	$-0.370956\pi$
$827$	22.6835	0.788782	0.394391	+	0.918943i	$0.370956\pi$
$828$	1.05226	0.0365685
$829$	−15.7594	−0.547347	−0.273674	−	0.961823i	$-0.588239\pi$
$829$	−15.7594	−0.547347	−0.273674	+	0.961823i	$0.588239\pi$
$830$	−2.25209	−0.0781712
$831$	−0.216358	−0.00750537
$832$	6.61830	0.229448
$833$	6.54219	0.226673
$834$	−0.172188	−0.00596237
$835$	2.29086	0.0792786
$836$	−3.64733	−0.126145
$837$	−0.433561	−0.0149860
$838$	13.7122	0.473680
$839$	3.35114	0.115694	0.0578471	−	0.998325i	$-0.481576\pi$
$839$	3.35114	0.115694	0.0578471	+	0.998325i	$0.481576\pi$
$840$	−0.0206116	−0.000711168 0
$841$	−25.2767	−0.871610
$842$	12.4715	0.429796
$843$	0.156907	0.00540418
$844$	4.12247	0.141901
$845$	−36.8111	−1.26634
$846$	−7.14570	−0.245674
$847$	−7.36732	−0.253144
$848$	−5.21338	−0.179028
$849$	−0.0495728	−0.00170133
$850$	−5.33289	−0.182917
$851$	0.298528	0.0102334
$852$	0.0803349	0.00275223
$853$	−11.8568	−0.405971	−0.202985	−	0.979182i	$-0.565064\pi$
$853$	−11.8568	−0.405971	−0.202985	+	0.979182i	$0.565064\pi$
$854$	−20.3301	−0.695683
$855$	5.14994	0.176124
$856$	−0.466778	−0.0159542
$857$	31.5053	1.07620	0.538100	−	0.842881i	$-0.319142\pi$
$857$	31.5053	1.07620	0.538100	+	0.842881i	$0.319142\pi$
$858$	−0.179112	−0.00611480
$859$	39.8586	1.35996	0.679979	−	0.733231i	$-0.261989\pi$
$859$	39.8586	1.35996	0.679979	+	0.733231i	$0.261989\pi$
$860$	−8.64982	−0.294956
$861$	−0.0432639	−0.00147443
$862$	12.6963	0.432439
$863$	31.2777	1.06471	0.532353	−	0.846522i	$-0.321308\pi$
$863$	31.2777	1.06471	0.532353	+	0.846522i	$0.321308\pi$
$864$	−0.0639505	−0.00217564
$865$	−17.2418	−0.586238
$866$	−31.3752	−1.06617
$867$	0.157436	0.00534679
$868$	−10.9702	−0.372354
$869$	−38.6709	−1.31182
$870$	−0.0245791	−0.000833310 0
$871$	−52.3312	−1.77318
$872$	11.4913	0.389145
$873$	−22.0176	−0.745181
$874$	0.503864	0.0170435
$875$	16.5760	0.560373
$876$	0.103041	0.00348143
$877$	42.4656	1.43396	0.716980	−	0.697094i	$-0.245524\pi$
$877$	42.4656	1.43396	0.716980	+	0.697094i	$0.245524\pi$
$878$	12.5412	0.423245
$879$	0.0761649	0.00256898
$880$	3.03444	0.102291
$881$	−6.18776	−0.208471	−0.104235	−	0.994553i	$-0.533240\pi$
$881$	−6.18776	−0.208471	−0.104235	+	0.994553i	$0.533240\pi$
$882$	−13.1446	−0.442601
$883$	−57.0202	−1.91888	−0.959441	−	0.281911i	$-0.909032\pi$
$883$	−57.0202	−1.91888	−0.959441	+	0.281911i	$0.909032\pi$
$884$	−9.88161	−0.332354
$885$	0.107538	0.00361484
$886$	−6.44117	−0.216395
$887$	−9.37984	−0.314944	−0.157472	−	0.987523i	$-0.550334\pi$
$887$	−9.37984	−0.314944	−0.157472	+	0.987523i	$0.550334\pi$
$888$	−0.00907128	−0.000304412 0
$889$	−28.1982	−0.945738
$890$	−12.0997	−0.405582
$891$	−22.8492	−0.765478
$892$	26.4151	0.884443
$893$	−3.42165	−0.114501
$894$	0.141144	0.00472055
$895$	−0.927064	−0.0309883
$896$	−1.61812	−0.0540575
$897$	0.0247437	0.000826168 0
$898$	−35.3339	−1.17911
$899$	−13.0819	−0.436306
$900$	10.7149	0.357162
$901$	7.78395	0.259321
$902$	6.36931	0.212075
$903$	−0.124829	−0.00415406
$904$	9.74852	0.324231
$905$	−3.34518	−0.111198
$906$	0.0993481	0.00330062
$907$	−10.3388	−0.343294	−0.171647	−	0.985159i	$-0.554909\pi$
$907$	−10.3388	−0.343294	−0.171647	+	0.985159i	$0.554909\pi$
$908$	−24.7298	−0.820686
$909$	29.2701	0.970829
$910$	12.7985	0.424265
$911$	39.3472	1.30363	0.651815	−	0.758378i	$-0.274008\pi$
$911$	39.3472	1.30363	0.651815	+	0.758378i	$0.274008\pi$
$912$	−0.0153108	−0.000506990 0
$913$	4.78479	0.158354
$914$	19.2302	0.636078
$915$	0.160041	0.00529080
$916$	23.1209	0.763935
$917$	−13.4903	−0.445489
$918$	0.0954827	0.00315140
$919$	43.2140	1.42550	0.712749	−	0.701419i	$-0.247450\pi$
$919$	43.2140	1.42550	0.712749	+	0.701419i	$0.247450\pi$
$920$	−0.419197	−0.0138205
$921$	0.168365	0.00554780
$922$	−8.28130	−0.272730
$923$	−49.8827	−1.64191
$924$	0.0437914	0.00144063
$925$	3.03983	0.0999491
$926$	26.4724	0.869938
$927$	−8.91475	−0.292799
$928$	−1.92959	−0.0633418
$929$	30.1586	0.989470	0.494735	−	0.869044i	$-0.335265\pi$
$929$	30.1586	0.989470	0.494735	+	0.869044i	$0.335265\pi$
$930$	0.0863590	0.00283182
$931$	−6.29417	−0.206283
$932$	−18.9023	−0.619164
$933$	0.0154932	0.000507224 0
$934$	−22.9936	−0.752375
$935$	−4.53064	−0.148168
$936$	19.8542	0.648954
$937$	−14.2354	−0.465050	−0.232525	−	0.972590i	$-0.574699\pi$
$937$	−14.2354	−0.465050	−0.232525	+	0.972590i	$0.574699\pi$
$938$	12.7945	0.417756
$939$	0.124101	0.00404990
$940$	2.84669	0.0928489
$941$	−32.3906	−1.05590	−0.527952	−	0.849274i	$-0.677040\pi$
$941$	−32.3906	−1.05590	−0.527952	+	0.849274i	$0.677040\pi$
$942$	0.0611610	0.00199273
$943$	−0.879897	−0.0286534
$944$	8.44227	0.274772
$945$	−0.123667	−0.00402290
$946$	18.3774	0.597501
$947$	−6.84695	−0.222496	−0.111248	−	0.993793i	$-0.535485\pi$
$947$	−6.84695	−0.222496	−0.111248	+	0.993793i	$0.535485\pi$
$948$	−0.162333	−0.00527234
$949$	−63.9817	−2.07693
$950$	5.13072	0.166463
$951$	0.262858	0.00852376
$952$	2.41597	0.0783019
$953$	8.59617	0.278457	0.139229	−	0.990260i	$-0.455538\pi$
$953$	8.59617	0.278457	0.139229	+	0.990260i	$0.455538\pi$
$954$	−15.6395	−0.506349
$955$	13.1093	0.424208
$956$	−16.7805	−0.542719
$957$	0.0522208	0.00168806
$958$	−2.41181	−0.0779220
$959$	−24.7403	−0.798905
$960$	0.0127380	0.000411118 0
$961$	14.9634	0.482690
$962$	5.63267	0.181605
$963$	−1.40028	−0.0451234
$964$	−28.3703	−0.913747
$965$	15.4066	0.495957
$966$	−0.00604962	−0.000194643 0
$967$	25.6715	0.825540	0.412770	−	0.910835i	$-0.364561\pi$
$967$	25.6715	0.825540	0.412770	+	0.910835i	$0.364561\pi$
$968$	4.55302	0.146340
$969$	0.0228601	0.000734372 0
$970$	8.77133	0.281630
$971$	11.4543	0.367585	0.183793	−	0.982965i	$-0.441163\pi$
$971$	11.4543	0.367585	0.183793	+	0.982965i	$0.441163\pi$
$972$	−0.287768	−0.00923017
$973$	−26.1404	−0.838021
$974$	7.66671	0.245657
$975$	0.251959	0.00806914
$976$	12.5641	0.402166
$977$	−28.0715	−0.898088	−0.449044	−	0.893510i	$-0.648235\pi$
$977$	−28.0715	−0.898088	−0.449044	+	0.893510i	$0.648235\pi$
$978$	−0.150570	−0.00481471
$979$	25.7069	0.821598
$980$	5.23653	0.167275
$981$	34.4726	1.10063
$982$	4.83529	0.154300
$983$	−9.08254	−0.289688	−0.144844	−	0.989455i	$-0.546268\pi$
$983$	−9.08254	−0.289688	−0.144844	+	0.989455i	$0.546268\pi$
$984$	0.0267372	0.000852350 0
$985$	7.05965	0.224939
$986$	2.88101	0.0917502
$987$	0.0410819	0.00130765
$988$	9.50699	0.302458
$989$	−2.53877	−0.0807282
$990$	9.10299	0.289312
$991$	12.5316	0.398079	0.199040	−	0.979991i	$-0.436218\pi$
$991$	12.5316	0.398079	0.199040	+	0.979991i	$0.436218\pi$
$992$	6.77963	0.215253
$993$	−0.139151	−0.00441583
$994$	12.1959	0.386830
$995$	−9.54317	−0.302539
$996$	0.0200856	0.000636438 0
$997$	40.0599	1.26871	0.634355	−	0.773042i	$-0.281266\pi$
$997$	40.0599	1.26871	0.634355	+	0.773042i	$0.281266\pi$
$998$	34.8875	1.10434
$999$	−0.0544266	−0.00172198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.21	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.21	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0106586 q^{3} +1.00000 q^{4} -1.19509 q^{5} +0.0106586 q^{6} +1.61812 q^{7} -1.00000 q^{8} -2.99989 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0106586 q^{3} +1.00000 q^{4} -1.19509 q^{5} +0.0106586 q^{6} +1.61812 q^{7} -1.00000 q^{8} -2.99989 q^{9} +1.19509 q^{10} -2.53909 q^{11} -0.0106586 q^{12} +6.61830 q^{13} -1.61812 q^{14} +0.0127380 q^{15} +1.00000 q^{16} -1.49307 q^{17} +2.99989 q^{18} +1.43647 q^{19} -1.19509 q^{20} -0.0172469 q^{21} +2.53909 q^{22} -0.350766 q^{23} +0.0106586 q^{24} -3.57176 q^{25} -6.61830 q^{26} +0.0639505 q^{27} +1.61812 q^{28} +1.92959 q^{29} -0.0127380 q^{30} -6.77963 q^{31} -1.00000 q^{32} +0.0270632 q^{33} +1.49307 q^{34} -1.93380 q^{35} -2.99989 q^{36} -0.851075 q^{37} -1.43647 q^{38} -0.0705420 q^{39} +1.19509 q^{40} +2.50850 q^{41} +0.0172469 q^{42} +7.23779 q^{43} -2.53909 q^{44} +3.58514 q^{45} +0.350766 q^{46} -2.38199 q^{47} -0.0106586 q^{48} -4.38170 q^{49} +3.57176 q^{50} +0.0159141 q^{51} +6.61830 q^{52} -5.21338 q^{53} -0.0639505 q^{54} +3.03444 q^{55} -1.61812 q^{56} -0.0153108 q^{57} -1.92959 q^{58} +8.44227 q^{59} +0.0127380 q^{60} +12.5641 q^{61} +6.77963 q^{62} -4.85417 q^{63} +1.00000 q^{64} -7.90948 q^{65} -0.0270632 q^{66} -7.90704 q^{67} -1.49307 q^{68} +0.00373868 q^{69} +1.93380 q^{70} -7.53708 q^{71} +2.99989 q^{72} -9.66738 q^{73} +0.851075 q^{74} +0.0380700 q^{75} +1.43647 q^{76} -4.10855 q^{77} +0.0705420 q^{78} +15.2302 q^{79} -1.19509 q^{80} +8.99898 q^{81} -2.50850 q^{82} -1.88445 q^{83} -0.0172469 q^{84} +1.78436 q^{85} -7.23779 q^{86} -0.0205667 q^{87} +2.53909 q^{88} -10.1245 q^{89} -3.58514 q^{90} +10.7092 q^{91} -0.350766 q^{92} +0.0722615 q^{93} +2.38199 q^{94} -1.71671 q^{95} +0.0106586 q^{96} +7.33946 q^{97} +4.38170 q^{98} +7.61698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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